Comparative study compact scheme for the case of shock tube problem

In this work, a high-order compact upwind scheme is developed for solving one-dimensional Euler equation. A detailed investigation was conducted to assess the performance of the basic third-order compact central discretization schemes. From this observation, discretization of the convective flux terms of the Euler equation is based on a hybrid flux-vector splitting, known as the advection upstream splitting method (AUSM) scheme which combines the accuracy of flux-difference splitting and the robustness of flux-vector splitting. In one-dimensional problem for the first order schemes, an explicit method is adopted by using time integration method. In addition to that, development and modification of source code for the one-dimensional flow is validated with two test cases namely, unsteady shock tube and quasi-one-dimensional supersonic-subsonic nozzle flow were using as a comparative study. Further analysis had also been done in comparing the characteristic of AUSM scheme against experimental results, obtained from previous works and also comparative analysis with computational results generated by van Leer, KFVS and AUSMPW schemes. Furthermore, there is a remarkable improvement with the extension of the AUSM scheme from firstorder to third-order accuracy in terms of shocks, contact discontinuities and rarefaction waves